Two children have two lollipops each. Each child can observe his or her own strength but not the other child’s strength, where each child’s strength is uniformly distributed between 0 and 1. The two children simultaneously decide whether or not to quarrel. If at least one child decides to quarrel, then the stronger child gets all four lollipops and the weaker child gets none. If neither child wants to quarrel, they each end up with two lollipops.

a. Formulate this situation as a Bayesian game.
b. Find all Nash equilibria of this game.
c. How would your answer to (b) change if one of the lollipops is destroyed when the children quarrel, such that the stronger child only gets three?
d. How would your answer to (b) change if child A decides first whether to quarrel or not, then child B, observing A’s choice, chooses whether to quarrel or not? (Again, a quarrel happens if and only if at least one child chooses to quarrel.)

Consider a small island country whose only industry is weaving. the following table shows information about the small economy in two different years. complete the table by calculating physical capital per worker as well as labor productivity. hint: recall that productivity is defined as the amount of goods and services a worker can produce per hour. in this problem, measure productivity as the quantity of goods per hour of labor. year physical capital labor force physical capital per worker labor hours output labor productivity (looms) (workers) (looms) (hours) (garments) (garments per hour of labor) 2024 160 40 1,800 14,400 2025 180 60 3,900 23,400

Who is better at multi-tasking? in business, employees are often asked to perform a complex task when their atten-tion is divided (i.e., multi-tasking). human factors (may 2014) published a study designed to determine whether video game players are better than non–video game play-ers at multi-tasking. each in a sample of 60 college stu-dents was classified as a video game player or a non-player. participants entered a street crossing simulator and were asked to cross a busy street at an unsigned intersec-tion. the simulator was designed to have cars traveling at various high rates of speed in both directions. during the crossing, the students also performed a memory task as a distraction. two variables were measured for each student: (1) a street crossing performance score (measured out of 100 points) and (2) a memory task score (measured out of 20 points). the researchers found no differences in either the street crossing performance or memory task score of video game players and non-gamers. “these results,” say the researchers, “suggest that action video game players [and non-gamers] are equally susceptible to the costs of dividing attention in a complex task”

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